Chris Huhne, the energy secretary, accused his cabinet colleague Lady Warsi of descending to Goebbels-like propaganda after she claimed the alternative vote would make mainstream parties pander to extremists such as the BNP.

Huhne exposed the tensions inside the cabinet over the 5 May referendum on the voting system earlier this week when he accused Warsi, the Tory party chairman, of gutter politics after she claimed the introduction of AV would cost more than £250m – so leading to the closure of hospitals.

The Lib Dem energy secretary went further in revealing the anger inside the yes campaign at the tactics being deployed by the no campaign, and Warsi in particular.

Huhne said: "If Baroness Warsi thinks that AV will benefit fascism she has to explain why the BNP wants to stick with what we have and Operation Black Vote supports AV. The BNP know the present system is their only chance of election.

"This is another example of the increasingly Goebbels-like campaign from the anti-AV people, for whom no lie is too idiotic given the truth is so unpalatable to them. AV makes lazy MPs work harder and reach out beyond their tribe. It is what Britain needs to clean up politics."

The exchanges reveal the extent to which the previously low-key manoeuvring over the AV referendum is beginning to turn into seriously hostile exchanges, with potentially long-term consequences for the coalition.

In a speech at Toynbee Hall in east London, Warsi claimed AV represented a threat to democracy, rewarded extremists and gave the oxygen of publicity to fascists.

She said: "AV gives more power to those people – fringe voters, Monster Raving Loonies, and yes, fascists – who are voting for precisely the kind of extreme policies most people want to marginalise.

"You don't need me to tell you that this represents a serious danger to our democracy. It means that bigots will be given more power in our politics and extremists will look to gain more influence over mainstream parties. The danger is that under AV, our whole political system would take a giant leap backwards, becoming more warped and disproportionate as fringe voters hold sway."

Warsi also claimed that to win, candidates would need to win the support of those whose first choices had been eliminated – and in many seats, that meant the BNP. She argued that in many seats where it takes a number of counts to reach a position in which one candidate gains more than 50% of the vote, the votes of extremists parties would be counted more than the vote of the mainstream candidate who eventually wins. She later accepted that the vote for the winning mainstream candidate would be counted in each round, but then argued the extremist candidate would determine the ultimate outcome.

The no campaign is increasingly optimistic that this argument holds sway with the public, especially among mainstream voters.

David Cameron has sanctioned a big fundraising exercise in an attempt to defeat the AV campaign and is under pressure from backbench MPs to do more to put the case personally.

It is understood that Nick Clegg, the Liberal Democrat leader, is not going to lie low in the referendum and will take a high-profile stance on the issue.

Independent polling expert Rob Hayward has predicted that the coalition is likely to lose as many as 1,000 seats to Labour in the local elections, with most seats being lost by the Conservatives.